TY - JOUR

T1 - Euler's constants for the Selberg and the Dedekind zeta functions

AU - Hashimoto, Yasufumi

AU - Iijima, Yasuyuki

AU - Kurokawa, Nobushige

AU - Wakayama, Masato

PY - 2004

Y1 - 2004

N2 - The purpose of this paper is to study an analogue of Euler's constant for the Selberg zeta functions of a compact Riemann surface and the Dedekind zeta function of an algebraic number field. Especially, we establish similar expressions of such Euler's constants as de la Vallée-Poussin obtained in 1896 for the Riemann zeta function. We also discuss, so to speak, higher Euler's constants and establish certain formulas concerning the power sums of essential zeroes of these zeta functions similar to Riemann's explicit formula.

AB - The purpose of this paper is to study an analogue of Euler's constant for the Selberg zeta functions of a compact Riemann surface and the Dedekind zeta function of an algebraic number field. Especially, we establish similar expressions of such Euler's constants as de la Vallée-Poussin obtained in 1896 for the Riemann zeta function. We also discuss, so to speak, higher Euler's constants and establish certain formulas concerning the power sums of essential zeroes of these zeta functions similar to Riemann's explicit formula.

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U2 - 10.36045/bbms/1102689119

DO - 10.36045/bbms/1102689119

M3 - Article

AN - SCOPUS:12944335053

SN - 1370-1444

VL - 11

SP - 493

EP - 516

JO - Bulletin of the Belgian Mathematical Society - Simon Stevin

JF - Bulletin of the Belgian Mathematical Society - Simon Stevin

IS - 4

ER -